Labour's leadership has been warned by a senior Blairite that it would be a mistake to believe that the country's voters have moved to the left.

Dame Tessa Jowell did not single out party leader Ed Miliband, but said some of those who supported his One Nation Labour vision believed that there had been a shift to the left.

She said Mr Miliband was "developing" the kind of presence Tony Blair had, and insisted: "I believe Ed will be prime minister".

In a call to stick to the centre ground, she told The Huffington Post: " I think one of the areas of debate about the differences between New Labour and One Nation Labour is that there are those who subscribe to One Nation Labour who would say that the country has moved to the left. I don't think that's true."

She backed Labour's plan to restore the 50p rate of income tax for top earners, saying people "have got to feel the road to recovery is equally being shared [and] is fair".

She added: " I think it is more a fairness message than it is a fiscal message, actually."

Dame Tessa, who is stepping down as an MP in 2015 and has been tipped as a potential candidate for London mayor, defended the record of New Labour in office.

Mr Miliband has said Labour "got things wrong" on immigration, but Dame Tessa said the problem was a failure to communicate with people.

"I'm not on the apologising side of this. Because I was there throughout and what I don't accept is that these were decisions that were taken recklessly," she said.

Referring to the introduction of a points-based immigration system in 2008, she said she told colleagues "we're going to have to go out and explain this, day in, day out, for the next six months" but "it didn't happen".

Dame Tessa said: "I think its been our failure to explain, our failure to reassure, our failure to confront real and legitimate anxieties that has gotten us into this position."

She also defended Labour's record on spending: "We inherited public infrastructure that was desperately in need [of modernisation] ... when we were elected, half of our hospitals had been built before 1880. That's why I don't accept we overspent."